The q-factorial is the q-analog of the factorial function.[1] It is written or and is defined as

As with all q-analogs, letting produces the ordinary factorial.

Based on the q-factorial, we can define the q-exponential function:

as well as q-trigonometric functions , , etc.

Values

1 2 3 4
1 1 1 1 1
2 2 3 4 5
3 6 21 52 105
4 24 315 2,080 8,925
5 120 9,765 251,680 3,043,425

Sources

See also

Main article: Factorial
Multifactorials: Double factorial · Multifactorial
Falling and rising: Falling factorial · Rising factorial
Other mathematical variants: Alternating factorial · Hyperfactorial · q-factorial · Roman factorial · Subfactorial · Weak factorial · Primorial · Compositorial · Semiprimorial
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Nested Factorials: Tetorial · Petorial · Ectorial · Zettorial · Yottorial
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial
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